The use of communication systems in both personal and business day-to-day tasks has become nearly ubiquitous. Both wireline communications networks and wireless communications networks, including the public switched telephone network (PSTN), the Internet, cellular networks, cable transmission systems, local area networks (LANs), metropolitan area networks (MANs), and wide area networks (WANs), are pervasively deployed in modern society and facilitate communication of voice, data, multimedia, etc.
In operation, the communication systems providing such communications implement various signal processing techniques, such as to up-convert and/or down-convert signals between baseband frequencies and carrier and/or intermediate frequencies, to modulate and/or demodulate the signals, to provide filtering and shaping of signals, to provide interference cancellation and/or mitigation, etc. Often, continuous signal sampling is implemented, such as for analog to digital conversion. Such continuous signal sampling is frequently required to be sampled with a sampling frequency significantly higher than the Nyquist frequency (i.e., oversampling). The oversampled signals are typically down-sampled to a lower frequency for the further processing in baseband. For example, a decimator module may be utilized to implement down-sampling of an oversampled signal to provide a baseband signal for further processing by other modules of a particular communication system.
Due to its relative simplicity, a Cascaded-Integrator-Comb (CIC) decimator is one of the most common decimators used with respect to down-sampling oversampled signals. In general, a CIC decimator is comprised of one or more integrator and comb filter pairs. In providing decimation of the oversampled single, the input signal is fed through one or more cascaded integrators, a down-sampler, and one or more comb sections (equal in number to the number of integrators). FIG. 1A shows a block diagram of CIC decimator 100A implemented as a L-stage CIC filter with differential delay M and decimator factor R. The frequency response of such a CIC filter may be represented as
                    H        CIC            ⁡              (                  ⅇ          jω                )              =                  [                              1            -                          ⅇ                                                -                  jω                                ⁢                                                                  ⁢                rRM                                                          1            -                          ⅇ                              -                jω                                                    ]            L        ,where R is the decimation ratio, M is the number of samples per stage, L is the number of stages in the filter. As can be appreciated from the diagram of FIG. 1A, digital implementation of CIC filters requires only additions and subtractions, which dramatically reduces the power consumption and hardware resource requirements as compared to other decimators.
FIGS. 2A and 2B illustrate the magnitude response of CIC decimators having different stages. Specifically, FIG. 2A generally illustrates the magnitude response of CIC decimators while FIG. 2B provides a magnified view of the passband of the CIC decimators. As can be appreciated from the graphs of FIG. 2A, the CIC filter exhibits a high passband drop and low stopband attenuation. Although the stopband attenuation can be increased with an increase in the number of stages, the drop in passband correspondingly becomes worse, which is not acceptable in many applications. From FIGS. 2A and 2B it is clear that, to obtain the target frequency response, extra linear phase filtering is necessary to compensate for the passband drop and to improve stopband attenuation. Accordingly, CIC decimator 100B shown in FIG. 1B includes compensation filter 101 coupled to the output of the CIC filter thereof to provide some level of linear phase filtering.
Several prior attempts have been made at addressing the design of the foregoing compensation filter. Some such attempts, however, only considered the passband drop. For example, the compensation filter design provided in U.S. Pat. No. 6,279,019 employs interpolated second-order polynomials to compensate for the passband drop, wherein the stopband attenuation is not improved or even made worse. Likewise, some prior attempts only consider the stopband attenuation. For example, the compensation filter design provided in U.S. Pat. No. 6,993,464 employs a Finite Impulse Response (FIR) filter design for spectral shaping by window methods to increase the stopband attenuation, wherein the passband drop is not improved or even made worse. Although some prior attempts have considered both the passband drop and stopband attenuation, such attempts have nevertheless provided undesirable implementations. For example, the compensation filter design provided in U.S. Pat. No. 7,035,888 employs a high order sharpening polynomial, wherein the wider the passband and the larger the stopband attenuation, the higher the order of the polynomial. Implementation using such higher order polynomials inevitably require multipliers, thus resulting in a relatively complex and resource costly solution. In “Understanding CIC Compensation Filters”, Altera, Application Note 455, April 2007, passband and stopband improvement is based on FIR filters. However, the frequency characteristic of CIC filter is not fully utilized during compensation filter design.